There is no royal road to geometry.

A youth who had begun to read geometry with Euclid, when he had learnt the first proposition, inquired, "What do I get by learning these things?" So Euclid called a slave and said "Give him threepence, since he must make a gain out of what he learns."

Stobaeus, *Extracts*

That, if a straight line falling on two straight lines makes
the interior angles on the same side less than two right angles,
the two straight lines, if produced indefinitely, meet on that
side on which the angles are less than two right angles.

[the 5th postulate]

JOC/EFR February 2006

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